The recent work of
[1]} proved that the \(L^2\)  norm of the error is bounded as \(\Vert f-\hat{f}_n\Vert _{L^2}=\mathcal {O}(n^{-\frac{d}{2d-1}})\) , for a two layer neural network with ReLU activation functions in kernel regimes. [2]} decomposed the \(L^2\)  norm of the error into a series corresponding to eigenfunctions of the NT kernel and provided bounds based on the corresponding eigenvalues. our results are stronger as they are given in terms of absolute error instead of \(L^2\)  norm. In addition, we provide explicit error bounds depending on differentiability of the activation functions.
